A senator wishes to estimate the proportion of United States voters who favor abolishing the Electoral College.How large a sample is needed in order to be 99% confident that the sample proportion will not differ from thetrue proportion by more than 3%?
A) 1842
B) 1509
C) 22
D) 3684

Question

Quizplus · Accepted Answer

The sample size needed for estimating a proportion with a specific margin of error (E) at a certain confidence level can be calculated using the formula: $n = \frac{Z^2 \cdot p \cdot (1-p)}{E^2}$, where Z is the Z-score corresponding to the confidence level (for 99% confidence, Z ≈ 2.576), p is the estimated proportion (when unknown, p = 0.5 is used for maximum sample size), and E is the margin of error. Plugging in the values: $n = \frac{2.576^2 \cdot 0.5 \cdot (1-0.5)}{0.03^2}$ gives a value close to 1842, rounding up for fractions.

A Senator Wishes to Estimate the Proportion of United States